We have a food warehouse store of sorts that sells corned beef made from the inside round. It's truly wonderful stuff. But be aware, the ability to eat the meat is dependent on how it's cooked, and how it's sliced. The outside round will work just fine if it's cooked properly, that is, low and slow, and no boiling. Typically, the corned beef made from the rounds is cut paper thin and layerd into sandwiches, rather than used in boiled dinner, or as a slice to place on a plate.
While in the U.S. Navy, aboard an aircraft carrier, I once had corned beef between two slices of bread that was so tough, it was nearly inedible (for most it wold have been, but I'm stubborn
). This meat was so tough that it wouldn't cut with a steak knife. And tearing it with my teeth was like tearing a piece of car tire, litteraly. I've never had such a tough piece of meat before or since.
I only bring this up as outside and bottom round can be extremely tough, hence the paper thin slices, and I'm not talking printer paper, but rather, tissue paper.
So yes, use you rounds, but follow the rules when cooking. Corning doesn't make it tender. Cooking and serving properly does.
Seeeeeya; Goodweed of the North